Subgroups — C₂₃×#60997 #19208623

Order 5888.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3256	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3242	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3241	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3232	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3220	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3204	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3203	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3198	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3198	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3179	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3178	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3174	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#3119	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#3111	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#553	—	2	1	no	—
35	C₂₃×#553	—	2	1	no	—
36	C₂₃×#553	—	2	1	no	—
37	C₂₃×#553	—	2	1	no	—
38	C₂₃×#552	—	2	1	no	—
39	C₂₃×#552	—	2	1	no	—
40	C₂₃×#544	C₂²	1	1	yes	characteristic
41	C₂₃×#542	—	2	1	no	—
42	C₂₃×#542	C₂²	1	1	yes	characteristic
43	C₂₃×#542	C₂²	1	1	yes	characteristic
44	C₂₃×#541	C₂²	1	1	yes	characteristic
45	C₂₃×#541	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#540	—	2	1	no	—
47	C₂₃×#540	C₂²	1	1	yes	characteristic
48	C₂₃×#540	C₂²	1	1	yes	characteristic
49	C₂₃×#540	C₂²	1	1	yes	characteristic
50	C₂₃×#540	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#538	—	2	1	no	—
52	C₂₃×#538	—	2	1	no	—
53	C₂₃×#537	C₂²	1	1	yes	characteristic
54	C₂₃×#537	C₂²	1	1	yes	characteristic
55	C₂₃×#537	C₂²	1	1	yes	characteristic
56	C₂₃×#535	C₂²	1	1	yes	characteristic
57	C₂₃×#535	C₂²	1	1	yes	characteristic
58	C₂₃×#532	—	2	1	no	—
59	C₂₃×#532	C₂²	1	1	yes	characteristic
60	C₂₃×#532	C₂²	1	1	yes	characteristic
61	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#529	—	2	1	no	—
63	C₂₃×#529	C₂²	1	1	yes	characteristic
64	C₂₃×#529	C₂²	1	1	yes	characteristic
65	C₂₃×#529	C₂²	1	1	yes	characteristic
66	C₂₃×#529	C₂²	1	1	yes	characteristic
67	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#525	—	2	1	no	—
71	C₂₃×#525	—	2	1	no	—
72	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
74	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
75	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#497	C₂²	1	1	yes	characteristic
82	C₂₃×#496	C₂²	1	1	yes	characteristic
83	C₂₃×#493	C₂²	1	1	yes	characteristic
84	C₂₃×#492	C₂²	1	1	yes	characteristic
85	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#490	C₂²	1	1	yes	characteristic
87	C₂₃×#490	C₂²	1	1	yes	characteristic
88	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#488	C₂²	1	1	yes	characteristic
90	C₂₃×#488	C₂²	1	1	yes	characteristic
91	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#485	C₂²	1	1	yes	characteristic
94	C₂₃×#485	C₂²	1	1	yes	characteristic
95	C₂₃×#484	C₂²	1	1	yes	characteristic
96	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#483	C₂²	1	1	yes	characteristic
98	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#482	C₂²	1	1	yes	characteristic
100	C₂₃×#482	C₂²	1	1	yes	characteristic
101	C₂₃×#481	C₂²	1	1	yes	characteristic
102	C₂₃×#481	C₂²	1	1	yes	characteristic
103	C₂₃×#481	C₂²	1	1	yes	characteristic
104	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#480	C₂²	1	1	yes	characteristic
106	C₂₃×#480	C₂²	1	1	yes	characteristic
107	C₂₃×#480	C₂²	1	1	yes	characteristic
108	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#478	C₂²	1	1	yes	characteristic
114	C₂₃×#478	C₂²	1	1	yes	characteristic
115	C₂₃×#478	C₂²	1	1	yes	characteristic
116	C₂₃×#478	C₂²	1	1	yes	characteristic
117	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
118	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
121	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
126	C₂₃×#469	C₂²	1	1	yes	characteristic
127	C₂₃×#469	C₂²	1	1	yes	characteristic
128	C₂₃×#469	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#468	C₂²	1	1	yes	characteristic
130	C₂₃×#468	C₂²	1	1	yes	characteristic
131	C₂₃×#468	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#468	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#466	C₂²	1	1	yes	characteristic
135	C₂₃×#466	C₂²	1	1	yes	characteristic
136	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
137	C₂₃×#465	C₂²	1	1	yes	characteristic
138	C₂₃×#465	C₂²	1	1	yes	characteristic
139	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
140	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
141	C₂₃×#464	C₂²	1	1	yes	characteristic
142	C₂₃×#464	C₂²	1	1	yes	characteristic
143	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
144	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
145	C₂₃×#463	C₂²	1	1	yes	characteristic
146	C₂₃×#463	C₂²	1	1	yes	characteristic
147	C₂₃×#463	C₂²	1	1	yes	characteristic
148	C₂₃×#463	C₂²	1	1	yes	characteristic
149	C₂₃×#463	C₂²	1	1	yes	characteristic
150	C₂₃×#463	C₂²	1	1	yes	characteristic
151	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
152	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
153	C₂₃×#460	C₂²	1	1	yes	characteristic
154	C₂₃×#460	C₂²	1	1	yes	characteristic
155	C₂₃×#459	C₂²	1	1	yes	characteristic
156	C₂₃×#459	C₂²	1	1	yes	characteristic
157	C₂₃×#452	C₂²	1	1	yes	characteristic
158	C₂₃×#452	C₂²	1	1	yes	characteristic
159	C₂₃×#452	C₂²	1	1	yes	characteristic, complemented
160	C₂₃×#452	C₂²	1	1	yes	characteristic, complemented
161	C₂₃×#450	C₂²	1	1	yes	characteristic
162	C₂₃×#450	C₂²	1	1	yes	characteristic
163	C₂₃×#449	C₂²	1	1	yes	characteristic
164	C₂₃×#449	C₂²	1	1	yes	characteristic
165	C₂₃×#449	C₂²	1	1	yes	characteristic
166	C₂₃×#449	C₂²	1	1	yes	characteristic
167	C₂₃×#449	C₂²	1	1	yes	characteristic
168	C₂₃×#449	C₂²	1	1	yes	characteristic
169	C₂₃×#449	C₂²	1	1	yes	characteristic, complemented
170	C₂₃×#449	C₂²	1	1	yes	characteristic, complemented
171	C₂₃×#447	C₂²	1	1	yes	characteristic
172	C₂₃×#447	C₂²	1	1	yes	characteristic
173	C₂₃×#442	C₂²	1	1	yes	characteristic
174	C₂₃×#442	C₂²	1	1	yes	characteristic
175	C₂₃×#442	C₂²	1	1	yes	characteristic, complemented
176	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
177	C₂₃×#440	C₂²	1	1	yes	characteristic
178	C₂₃×#440	C₂²	1	1	yes	characteristic
179	C₂₃×#440	C₂²	1	1	yes	characteristic, complemented
180	C₂₃×#440	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
183	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
184	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
187	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
188	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
189	C₂₃×#433	C₂²	1	1	yes	characteristic
190	C₂₃×#433	C₂²	1	1	yes	characteristic
191	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
192	C₂₃×#433	C₂²	1	1	yes	characteristic, complemented
193	C₂₃×#432	C₂²	1	1	yes	characteristic
194	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
195	C₂₃×#431	C₂²	1	1	yes	characteristic
196	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
197	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
198	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
199	C₂₃×#408	C₂²	1	1	yes	characteristic
200	C₂₃×#408	C₂²	1	1	yes	characteristic
201	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
202	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₂₃	—	2	1	no	—
204	C₂×#41×C₂₃	—	2	1	no	—
205	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
209	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₂₃	—	2	1	no	—
211	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
222	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
229	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
230	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
231	C₂₃×C₄⋊Q₈	—	2	1	no	—
232	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
233	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
234	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂₃×#127	—	2	1	no	—
236	C₂₃×#127	C₂³	1	1	yes	characteristic
237	C₂₃×#127	C₂³	1	1	yes	characteristic
238	C₂₃×#127	C₂³	1	1	yes	characteristic
239	C₂₃×#126	—	2	1	no	—
240	C₂₃×#126	—	2	1	no	—
241	C₂₃×#126	—	2	1	no	—
242	C₂₃×#126	—	2	1	no	—
243	C₂₃×#126	—	2	1	no	—
244	C₂₃×#126	—	2	1	no	—
245	C₂₃×#126	—	2	1	no	—
246	C₂₃×#126	—	2	1	no	—
247	C₂₃×#126	—	2	1	no	—
248	C₂₃×#126	—	2	1	no	—
249	C₂₃×#126	—	2	1	no	—
250	C₂₃×#126	—	2	1	no	—
251	C₂₃×#125	—	2	1	no	—
252	C₂₃×#125	—	2	1	no	—
253	C₂₃×#125	—	2	1	no	—
254	C₂₃×#125	—	2	1	no	—
255	C₂₃×#125	—	2	1	no	—
256	C₂₃×#125	—	2	1	no	—
257	C₂₃×#125	—	2	1	no	—
258	C₂₃×#125	C₂³	1	1	yes	characteristic
259	C₂₃×#125	C₂³	1	1	yes	characteristic
260	C₂₃×#125	C₂³	1	1	yes	characteristic
261	C₂₃×#125	C₂³	1	1	yes	characteristic
262	C₂₃×#125	C₂³	1	1	yes	characteristic
263	C₂₃×#125	C₂³	1	1	yes	characteristic
264	C₂₃×#124	—	2	1	no	—
265	C₂₃×#124	—	2	1	no	—
266	C₂₃×#124	—	2	1	no	—
267	C₂₃×#124	—	2	1	no	—
268	C₂₃×#124	—	2	1	no	—
269	C₂₃×#124	C₂³	1	1	yes	characteristic
270	C₂₃×#124	C₂³	1	1	yes	characteristic
271	C₂₃×#124	C₂³	1	1	yes	characteristic
272	C₂₃×#124	C₂³	1	1	yes	characteristic
273	C₂₃×#123	—	2	1	no	—
274	C₂₃×#123	—	2	1	no	—
275	C₂₃×#123	—	2	1	no	—
276	C₂₃×#123	—	2	1	no	—
277	C₂₃×#123	—	2	1	no	—
278	C₂₃×#123	—	2	1	no	—
279	C₂₃×#123	—	2	1	no	—
280	C₂₃×#123	—	2	1	no	—
281	C₂₃×#123	—	2	1	no	—
282	C₂₃×#123	—	2	1	no	—
283	C₂₃×#123	—	2	1	no	—
284	C₂₃×#123	—	2	1	no	—
285	C₂₃×#123	—	2	1	no	—
286	C₂₃×#123	—	2	1	no	—
287	C₂₃×#123	—	2	1	no	—
288	C₂₃×#123	—	2	1	no	—
289	C₂₃×C₂²⋊Q₈	—	2	1	no	—
290	C₂₃×C₂²⋊Q₈	—	2	1	no	—
291	C₂₃×C₂²⋊Q₈	—	2	1	no	—
292	C₂₃×C₂²⋊Q₈	—	2	1	no	—
293	C₂₃×C₂²⋊Q₈	—	2	1	no	—
294	C₂₃×C₂²⋊Q₈	—	2	1	no	—
295	C₂₃×C₂²⋊Q₈	—	2	1	no	—
296	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
297	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
298	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
299	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
300	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
301	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
302	C₂₃×#121	—	2	1	no	—
303	C₂₃×#121	—	2	1	no	—
304	C₂₃×#121	—	2	1	no	—
305	C₂₃×#121	—	2	1	no	—
306	C₂₃×#121	—	2	1	no	—
307	C₂₃×#121	—	2	1	no	—
308	C₂₃×#121	—	2	1	no	—
309	C₂₃×#121	—	2	1	no	—
310	C₂₃×#121	—	2	1	no	—
311	C₂₃×#121	—	2	1	no	—
312	C₂₃×#121	—	2	1	no	—
313	C₂₃×#121	—	2	1	no	—
314	C₂₃×#121	—	2	1	no	—
315	C₂₃×#121	—	2	1	no	—
316	C₂₃×#121	—	2	1	no	—
317	C₂₃×#121	—	2	1	no	—
318	C₂₃×#121	—	2	1	no	—
319	C₂₃×#121	—	2	1	no	—
320	C₂₃×#121	—	2	1	no	—
321	C₂₃×#121	—	2	1	no	—
322	C₂₃×#121	—	2	1	no	—
323	C₂₃×#121	—	2	1	no	—
324	C₂₃×#121	—	2	1	no	—
325	C₂₃×#121	C₂³	1	1	yes	characteristic
326	C₂₃×#121	C₂³	1	1	yes	characteristic
327	C₂₃×#121	C₂³	1	1	yes	characteristic
328	C₂₃×#121	C₂³	1	1	yes	characteristic
329	C₂₃×#121	C₂³	1	1	yes	characteristic
330	C₂₃×#121	C₂³	1	1	yes	characteristic
331	C₂₃×#121	C₂³	1	1	yes	characteristic
332	C₂₃×#121	C₂³	1	1	yes	characteristic
333	C₂₃×#121	C₂³	1	1	yes	characteristic
334	C₂₃×#121	C₂³	1	1	yes	characteristic
335	C₂₃×#120	—	2	1	no	—
336	C₂₃×#120	—	2	1	no	—
337	C₂₃×#120	—	2	1	no	—
338	C₂₃×#120	—	2	1	no	—
339	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
340	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
341	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
347	C₄×D₄×C₂₃	—	2	1	no	—
348	C₄×D₄×C₂₃	—	2	1	no	—
349	C₄×D₄×C₂₃	—	2	1	no	—
350	C₄×D₄×C₂₃	—	2	1	no	—
351	C₄×D₄×C₂₃	—	2	1	no	—
352	C₄×D₄×C₂₃	—	2	1	no	—
353	C₄×D₄×C₂₃	—	2	1	no	—
354	C₄×D₄×C₂₃	—	2	1	no	—
355	C₄×D₄×C₂₃	—	2	1	no	—
356	C₄×D₄×C₂₃	—	2	1	no	—
357	C₄×D₄×C₂₃	—	2	1	no	—
358	C₄×D₄×C₂₃	—	2	1	no	—
359	C₄×D₄×C₂₃	—	2	1	no	—
360	C₄×D₄×C₂₃	—	2	1	no	—
361	C₄×D₄×C₂₃	—	2	1	no	—
362	C₄×D₄×C₂₃	—	2	1	no	—
363	C₄×D₄×C₂₃	—	2	1	no	—
364	C₄×D₄×C₂₃	—	2	1	no	—
365	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
366	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
367	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
368	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
369	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
370	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
371	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
377	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
379	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
381	C₂₃×#117	—	2	1	no	—
382	C₂₃×#117	—	2	1	no	—
383	C₂₃×#117	—	2	1	no	—
384	C₂₃×#117	—	2	1	no	—
385	C₂₃×#117	—	2	1	no	—
386	C₂₃×#117	—	2	1	no	—
387	C₂₃×#117	—	2	1	no	—
388	C₂₃×#117	—	2	1	no	—
389	C₂₃×#117	—	2	1	no	—
390	C₂₃×#117	C₂³	1	1	yes	characteristic
391	C₂₃×#117	C₂³	1	1	yes	characteristic
392	C₂₃×#117	C₂³	1	1	yes	characteristic
393	C₂₃×#117	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
399	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
401	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
402	C₂×C₄²×C₂₃	—	2	1	no	—
403	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
404	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
405	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
406	C₂₃×#107	C₂³	1	1	yes	characteristic
407	C₂₃×#107	C₂³	1	1	yes	characteristic
408	C₂₃×#107	C₂³	1	1	yes	characteristic
409	C₂₃×#107	C₂³	1	1	yes	characteristic
410	C₂₃×#107	C₂³	1	1	yes	characteristic
411	C₂₃×#107	C₂³	1	1	yes	characteristic
412	C₂₃×#107	C₂³	1	1	yes	characteristic
413	C₂₃×#107	C₂³	1	1	yes	characteristic
414	C₂₃×#106	C₂³	1	1	yes	characteristic
415	C₂₃×#106	C₂³	1	1	yes	characteristic
416	C₂₃×#106	C₂³	1	1	yes	characteristic
417	C₂₃×#106	C₂³	1	1	yes	characteristic
418	C₂₃×#106	C₂³	1	1	yes	characteristic
419	C₂₃×#106	C₂³	1	1	yes	characteristic
420	C₂₃×#106	C₂³	1	1	yes	characteristic
421	C₂₃×#106	C₂³	1	1	yes	characteristic
422	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
424	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₂₃×#103	C₂³	1	1	yes	characteristic
431	C₂₃×#103	C₂³	1	1	yes	characteristic
432	C₂₃×#103	C₂³	1	1	yes	characteristic
433	C₂₃×#103	C₂³	1	1	yes	characteristic
434	C₂₃×#103	C₂³	1	1	yes	characteristic
435	C₂₃×#103	C₂³	1	1	yes	characteristic
436	C₂₃×#103	C₂³	1	1	yes	characteristic
437	C₂₃×#103	C₂³	1	1	yes	characteristic
438	C₂₃×#103	C₂³	1	1	yes	characteristic
439	C₂₃×#103	C₂³	1	1	yes	characteristic
440	C₂₃×#103	C₂³	1	1	yes	characteristic
441	C₂₃×#103	C₂³	1	1	yes	characteristic
442	C₂₃×#102	C₂³	1	1	yes	characteristic
443	C₂₃×#102	C₂³	1	1	yes	characteristic
444	C₂₃×#102	C₂³	1	1	yes	characteristic
445	C₂₃×#102	C₂³	1	1	yes	characteristic
446	C₂₃×#102	C₂³	1	1	yes	characteristic
447	C₂₃×#102	C₂³	1	1	yes	characteristic
448	C₂₃×#102	C₂³	1	1	yes	characteristic
449	C₂₃×#102	C₂³	1	1	yes	characteristic
450	C₂₃×#102	C₂³	1	1	yes	characteristic
451	C₂₃×#102	C₂³	1	1	yes	characteristic
452	C₂₃×#102	C₂³	1	1	yes	characteristic
453	C₂₃×#102	C₂³	1	1	yes	characteristic
454	C₂₃×#102	C₂³	1	1	yes	characteristic
455	C₂₃×#102	C₂³	1	1	yes	characteristic
456	C₂₃×#102	C₂³	1	1	yes	characteristic
457	C₂₃×#102	C₂³	1	1	yes	characteristic
458	C₂₃×#102	C₂³	1	1	yes	characteristic
459	C₂₃×#102	C₂³	1	1	yes	characteristic
460	C₂₃×#102	C₂³	1	1	yes	characteristic
461	C₂₃×#102	C₂³	1	1	yes	characteristic
462	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₂₃×#97	C₂³	1	1	yes	characteristic
471	C₂₃×#97	C₂³	1	1	yes	characteristic
472	C₂₃×#97	C₂³	1	1	yes	characteristic
473	C₂₃×#97	C₂³	1	1	yes	characteristic
474	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
475	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
478	C₂⁴×C₂₃	—	2	1	no	—
479	#41×C₂₃	—	4	1	no	—
480	#41×C₂₃	—	4	1	no	—
481	#41×C₂₃	—	4	1	no	—
482	#41×C₂₃	—	4	1	no	—
483	#41×C₂₃	—	4	1	no	—
484	#41×C₂₃	—	4	1	no	—
485	#41×C₂₃	—	4	1	no	—
486	#41×C₂₃	—	4	1	no	—
487	#41×C₂₃	—	8	2	no	—
488	#41×C₂₃	—	8	2	no	—
489	C₂×Q₈×C₂₃	—	2	1	no	—
490	C₂×Q₈×C₂₃	—	2	1	no	—
491	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₂₃	—	2	1	no	—
496	C₂×D₄×C₂₃	—	2	1	no	—
497	C₂×D₄×C₂₃	—	2	1	no	—
498	C₂×D₄×C₂₃	—	2	1	no	—
499	C₂×D₄×C₂₃	—	2	1	no	—
500	C₂×D₄×C₂₃	—	2	1	no	—
501	C₂×D₄×C₂₃	—	2	1	no	—
502	C₂×D₄×C₂₃	—	2	1	no	—
503	C₂×D₄×C₂₃	—	2	1	no	—
504	C₂×D₄×C₂₃	—	2	1	no	—
505	C₂×D₄×C₂₃	—	2	1	no	—
506	C₂×D₄×C₂₃	—	2	1	no	—
507	C₂×D₄×C₂₃	—	2	1	no	—
508	C₂×D₄×C₂₃	—	2	1	no	—
509	C₂×D₄×C₂₃	—	2	1	no	—
510	C₂×D₄×C₂₃	—	2	1	no	—
511	C₂×D₄×C₂₃	—	2	1	no	—
512	C₂×D₄×C₂₃	—	2	1	no	—
513	C₂×D₄×C₂₃	—	2	1	no	—
514	C₂×D₄×C₂₃	—	2	1	no	—
515	C₂×D₄×C₂₃	—	4	1	no	—
516	C₂×D₄×C₂₃	—	4	1	no	—
517	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
520	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
521	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
522	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
523	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
524	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₂₃	—	2	1	no	—
526	C₂²×C₄×C₂₃	—	2	1	no	—
527	C₂²×C₄×C₂₃	—	2	1	no	—
528	C₂²×C₄×C₂₃	—	2	1	no	—
529	C₂²×C₄×C₂₃	—	2	1	no	—
530	C₂²×C₄×C₂₃	—	2	1	no	—
531	C₂²×C₄×C₂₃	—	2	1	no	—
532	C₂²×C₄×C₂₃	—	2	1	no	—
533	C₂²×C₄×C₂₃	—	2	1	no	—
534	C₂²×C₄×C₂₃	—	2	1	no	—
535	C₂²×C₄×C₂₃	—	2	1	no	—
536	C₂²×C₄×C₂₃	—	2	1	no	—
537	C₂²×C₄×C₂₃	—	2	1	no	—
538	C₂²×C₄×C₂₃	—	2	1	no	—
539	C₂²×C₄×C₂₃	—	2	1	no	—
540	C₂²×C₄×C₂₃	—	2	1	no	—
541	C₂²×C₄×C₂₃	—	8	2	no	—
542	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
543	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
544	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
545	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
546	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
547	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
548	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
549	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
550	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
551	Q₁₆×C₂₃	—	4	1	no	—
552	Q₁₆×C₂₃	—	4	1	no	—
553	SD₁₆×C₂₃	—	4	1	no	—
554	SD₁₆×C₂₃	—	4	1	no	—
555	SD₁₆×C₂₃	—	4	1	no	—
556	SD₁₆×C₂₃	—	4	1	no	—
557	SD₁₆×C₂₃	—	4	1	no	—
558	SD₁₆×C₂₃	—	4	1	no	—
559	SD₁₆×C₂₃	—	4	1	no	—
560	SD₁₆×C₂₃	—	4	1	no	—
561	D₈×C₂₃	—	4	1	no	—
562	D₈×C₂₃	—	4	1	no	—
563	D₈×C₂₃	—	4	1	no	—
564	D₈×C₂₃	—	4	1	no	—
565	D₈×C₂₃	—	4	1	no	—
566	D₈×C₂₃	—	4	1	no	—
567	M₁₆×C₂₃	—	4	1	no	—
568	M₁₆×C₂₃	—	4	1	no	—
569	C₂×C₈×C₂₃	—	4	1	no	—
570	C₂×C₈×C₂₃	—	4	1	no	—
571	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
572	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
573	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
574	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
575	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
576	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
577	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
578	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
579	C₄⋊C₄×C₂₃	—	2	1	no	—
580	C₄⋊C₄×C₂₃	—	2	1	no	—
581	C₄⋊C₄×C₂₃	—	2	1	no	—
582	C₄⋊C₄×C₂₃	—	2	1	no	—
583	C₄⋊C₄×C₂₃	—	2	1	no	—
584	C₄⋊C₄×C₂₃	—	2	1	no	—
585	C₄⋊C₄×C₂₃	—	2	1	no	—
586	C₄⋊C₄×C₂₃	—	2	1	no	—
587	C₄⋊C₄×C₂₃	—	2	1	no	—
588	C₄⋊C₄×C₂₃	—	2	1	no	—
589	C₄⋊C₄×C₂₃	—	2	1	no	—
590	C₄⋊C₄×C₂₃	—	2	1	no	—
591	C₄⋊C₄×C₂₃	—	2	1	no	—
592	C₄⋊C₄×C₂₃	—	2	1	no	—
593	C₄⋊C₄×C₂₃	—	2	1	no	—
594	C₄⋊C₄×C₂₃	—	2	1	no	—
595	C₄⋊C₄×C₂₃	—	2	1	no	—
596	C₄⋊C₄×C₂₃	—	2	1	no	—
597	C₄⋊C₄×C₂₃	—	2	1	no	—
598	C₄⋊C₄×C₂₃	—	2	1	no	—
599	C₄⋊C₄×C₂₃	—	2	1	no	—
600	C₄⋊C₄×C₂₃	—	2	1	no	—
601	C₄⋊C₄×C₂₃	—	2	1	no	—
602	C₄⋊C₄×C₂₃	—	2	1	no	—
603	C₄⋊C₄×C₂₃	—	2	1	no	—
604	C₄⋊C₄×C₂₃	—	2	1	no	—
605	C₄⋊C₄×C₂₃	—	2	1	no	—
606	C₄⋊C₄×C₂₃	—	2	1	no	—
607	C₄⋊C₄×C₂₃	—	2	1	no	—
608	C₄⋊C₄×C₂₃	—	2	1	no	—
609	C₄⋊C₄×C₂₃	—	2	1	no	—
610	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
616	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
621	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
622	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
623	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
624	C₂²⋊C₄×C₂₃	—	2	1	no	—
625	C₂²⋊C₄×C₂₃	—	2	1	no	—
626	C₂²⋊C₄×C₂₃	—	2	1	no	—
627	C₂²⋊C₄×C₂₃	—	2	1	no	—
628	C₂²⋊C₄×C₂₃	—	2	1	no	—
629	C₂²⋊C₄×C₂₃	—	2	1	no	—
630	C₂²⋊C₄×C₂₃	—	2	1	no	—
631	C₂²⋊C₄×C₂₃	—	2	1	no	—
632	C₂²⋊C₄×C₂₃	—	2	1	no	—
633	C₂²⋊C₄×C₂₃	—	2	1	no	—
634	C₂²⋊C₄×C₂₃	—	2	1	no	—
635	C₂²⋊C₄×C₂₃	—	2	1	no	—
636	C₂²⋊C₄×C₂₃	—	2	1	no	—
637	C₂²⋊C₄×C₂₃	—	2	1	no	—
638	C₂²⋊C₄×C₂₃	—	2	1	no	—
639	C₂²⋊C₄×C₂₃	—	2	1	no	—
640	C₂²⋊C₄×C₂₃	—	2	1	no	—
641	C₂²⋊C₄×C₂₃	—	2	1	no	—
642	C₂²⋊C₄×C₂₃	—	2	1	no	—
643	C₂²⋊C₄×C₂₃	—	2	1	no	—
644	C₂²⋊C₄×C₂₃	—	2	1	no	—
645	C₂²⋊C₄×C₂₃	—	2	1	no	—
646	C₂²⋊C₄×C₂₃	—	2	1	no	—
647	C₂²⋊C₄×C₂₃	—	2	1	no	—
648	C₂²⋊C₄×C₂₃	—	2	1	no	—
649	C₂²⋊C₄×C₂₃	—	2	1	no	—
650	C₂²⋊C₄×C₂₃	—	2	1	no	—
651	C₂²⋊C₄×C₂₃	—	2	1	no	—
652	C₂²⋊C₄×C₂₃	—	2	1	no	—
653	C₂²⋊C₄×C₂₃	—	2	1	no	—
654	C₂²⋊C₄×C₂₃	—	2	1	no	—
655	C₂²⋊C₄×C₂₃	—	2	1	no	—
656	C₂²⋊C₄×C₂₃	—	2	1	no	—
657	C₂²⋊C₄×C₂₃	—	2	1	no	—
658	C₂²⋊C₄×C₂₃	—	2	1	no	—
659	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
661	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
662	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
663	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
664	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
665	C₄²×C₂₃	—	2	1	no	—
666	C₄²×C₂₃	—	2	1	no	—
667	C₄²×C₂₃	—	2	1	no	—
668	C₄²×C₂₃	—	2	1	no	—
669	C₄²×C₂₃	—	2	1	no	—
670	C₄²×C₂₃	—	2	1	no	—
671	C₄²×C₂₃	—	2	1	no	—
672	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
673	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
674	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
675	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
676	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
677	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
678	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
679	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
680	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
681	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
682	#60997	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
683	C₂³×C₂₃	—	2	1	no	—
684	C₂³×C₂₃	—	2	1	no	—
685	C₂³×C₂₃	—	2	1	no	—
686	C₂³×C₂₃	—	2	1	no	—
687	C₂³×C₂₃	—	2	1	no	—
688	C₂³×C₂₃	—	4	2	no	—
689	C₂³×C₂₃	—	8	1	no	—
690	C₂³×C₂₃	—	8	1	no	—
691	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
692	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
693	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
694	Q₈×C₂₃	—	2	1	no	—
695	Q₈×C₂₃	—	2	1	no	—
696	Q₈×C₂₃	—	2	1	no	—
697	Q₈×C₂₃	—	2	1	no	—
698	Q₈×C₂₃	—	2	1	no	—
699	Q₈×C₂₃	—	2	1	no	—
700	Q₈×C₂₃	—	4	1	no	—
701	Q₈×C₂₃	—	8	1	no	—
702	Q₈×C₂₃	—	8	1	no	—
703	D₄×C₂₃	—	2	1	no	—
704	D₄×C₂₃	—	2	1	no	—
705	D₄×C₂₃	—	2	1	no	—
706	D₄×C₂₃	—	2	1	no	—
707	D₄×C₂₃	—	2	1	no	—
708	D₄×C₂₃	—	2	1	no	—
709	D₄×C₂₃	—	2	1	no	—
710	D₄×C₂₃	—	2	1	no	—
711	D₄×C₂₃	—	2	1	no	—
712	D₄×C₂₃	—	2	1	no	—
713	D₄×C₂₃	—	4	1	no	—
714	D₄×C₂₃	—	4	1	no	—
715	D₄×C₂₃	—	4	1	no	—
716	D₄×C₂₃	—	4	2	no	—
717	D₄×C₂₃	—	4	2	no	—
718	D₄×C₂₃	—	4	2	no	—
719	D₄×C₂₃	—	4	2	no	—
720	D₄×C₂₃	—	8	1	no	—
721	D₄×C₂₃	—	8	1	no	—
722	D₄×C₂₃	—	8	1	no	—
723	D₄×C₂₃	—	8	1	no	—
724	D₄×C₂₃	—	8	1	no	—
725	D₄×C₂₃	—	8	1	no	—
726	D₄×C₂₃	—	8	1	no	—
727	D₄×C₂₃	—	8	1	no	—
728	D₄×C₂₃	—	8	1	no	—
729	D₄×C₂₃	—	8	1	no	—
730	D₄×C₂₃	—	8	1	no	—
731	D₄×C₂₃	—	8	1	no	—
732	D₄×C₂₃	—	8	1	no	—
733	D₄×C₂₃	—	8	1	no	—
734	D₄×C₂₃	—	8	1	no	—
735	D₄×C₂₃	—	8	1	no	—
736	C₂×C₄×C₂₃	—	2	1	no	—
737	C₂×C₄×C₂₃	—	2	1	no	—
738	C₂×C₄×C₂₃	—	2	1	no	—
739	C₂×C₄×C₂₃	—	2	1	no	—
740	C₂×C₄×C₂₃	—	2	1	no	—
741	C₂×C₄×C₂₃	—	2	1	no	—
742	C₂×C₄×C₂₃	—	2	1	no	—
743	C₂×C₄×C₂₃	—	2	1	no	—
744	C₂×C₄×C₂₃	—	2	1	no	—
745	C₂×C₄×C₂₃	—	2	1	no	—
746	C₂×C₄×C₂₃	—	2	1	no	—
747	C₂×C₄×C₂₃	—	2	1	no	—
748	C₂×C₄×C₂₃	—	2	1	no	—
749	C₂×C₄×C₂₃	—	2	1	no	—
750	C₂×C₄×C₂₃	—	2	1	no	—
751	C₂×C₄×C₂₃	—	2	1	no	—
752	C₂×C₄×C₂₃	—	2	1	no	—
753	C₂×C₄×C₂₃	—	4	1	no	—
754	C₂×C₄×C₂₃	—	4	1	no	—
755	C₂×C₄×C₂₃	—	4	1	no	—
756	C₂×C₄×C₂₃	—	4	1	no	—
757	C₂×C₄×C₂₃	—	4	1	no	—
758	C₂×C₄×C₂₃	—	4	1	no	—
759	C₂×C₄×C₂₃	—	4	2	no	—
760	C₂×C₄×C₂₃	—	4	2	no	—
761	C₂×C₄×C₂₃	—	4	2	no	—
762	C₂×C₄×C₂₃	—	4	2	no	—
763	C₂×C₄×C₂₃	—	4	2	no	—
764	C₂×C₄×C₂₃	—	4	2	no	—
765	C₂×C₄×C₂₃	—	8	1	no	—
766	C₂×C₄×C₂₃	—	8	1	no	—
767	C₂×C₄×C₂₃	—	8	1	no	—
768	C₂×C₄×C₂₃	—	8	1	no	—
769	C₂×C₄×C₂₃	—	8	1	no	—
770	C₂×C₄×C₂₃	—	8	1	no	—
771	C₂×C₄×C₂₃	—	8	1	no	—
772	C₂×C₄×C₂₃	—	8	1	no	—
773	C₂×C₄×C₂₃	—	8	1	no	—
774	C₂×C₄×C₂₃	—	8	1	no	—
775	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
776	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
777	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
778	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
779	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
780	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
781	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
787	C₈×C₂₃	—	2	1	no	—
788	C₈×C₂₃	—	2	1	no	—
789	C₈×C₂₃	—	2	1	no	—
790	C₈×C₂₃	—	2	1	no	—
791	C₈×C₂₃	—	2	1	no	—
792	C₈×C₂₃	—	2	1	no	—
793	C₈×C₂₃	—	2	1	no	—
794	C₈×C₂₃	—	2	1	no	—
795	#3512	C₂×C₂₃	1	1	yes	characteristic, complemented
796	#3460	C₂×C₂₃	1	1	yes	characteristic, complemented
797	#3256	C₂×C₂₃	1	1	yes	characteristic, complemented
798	#3251	C₂×C₂₃	1	1	yes	characteristic, complemented
799	#3250	C₂×C₂₃	1	1	yes	characteristic, complemented
800	#3247	C₂×C₂₃	1	1	yes	characteristic, complemented
801	#3242	C₂×C₂₃	1	1	yes	characteristic, complemented
802	#3241	C₂×C₂₃	1	1	yes	characteristic, complemented
803	#3234	C₂×C₂₃	1	1	yes	characteristic, complemented
804	#3232	C₂×C₂₃	1	1	yes	characteristic, complemented
805	#3222	C₂×C₂₃	1	1	yes	characteristic, complemented
806	#3220	C₂×C₂₃	1	1	yes	characteristic, complemented
807	#3219	C₂×C₂₃	1	1	yes	characteristic, complemented
808	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
809	#3204	C₂×C₂₃	1	1	yes	characteristic, complemented
810	#3203	C₂×C₂₃	1	1	yes	characteristic, complemented
811	#3198	C₂×C₂₃	1	1	yes	characteristic, complemented
812	#3198	C₂×C₂₃	1	1	yes	characteristic, complemented
813	#3179	C₂×C₂₃	1	1	yes	characteristic, complemented
814	#3178	C₂×C₂₃	1	1	yes	characteristic, complemented
815	#3176	C₂×C₂₃	1	1	yes	characteristic, complemented
816	#3174	C₂×C₂₃	1	1	yes	characteristic, complemented
817	#3125	C₂×C₂₃	1	1	yes	characteristic, complemented
818	#3124	C₂×C₂₃	1	1	yes	characteristic, complemented
819	#3119	C₂×C₂₃	1	1	yes	characteristic, complemented
820	#3119	C₂×C₂₃	1	1	yes	characteristic, complemented
821	#3114	C₂×C₂₃	1	1	yes	characteristic, complemented
822	#3111	C₂×C₂₃	1	1	yes	characteristic, complemented
823	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
824	#3102	C₂×C₂₃	1	1	yes	characteristic, complemented
825	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
826	C₂²×C₂₃	—	2	1	no	—
827	C₂²×C₂₃	—	2	1	no	—
828	C₂²×C₂₃	—	2	1	no	—
829	C₂²×C₂₃	—	2	1	no	—
830	C₂²×C₂₃	—	2	1	no	—
831	C₂²×C₂₃	—	2	1	no	—
832	C₂²×C₂₃	—	2	1	no	—
833	C₂²×C₂₃	—	2	1	no	—
834	C₂²×C₂₃	—	2	1	no	—
835	C₂²×C₂₃	—	4	1	no	—
836	C₂²×C₂₃	—	4	1	no	—
837	C₂²×C₂₃	—	4	1	no	—
838	C₂²×C₂₃	—	4	1	no	—
839	C₂²×C₂₃	—	4	1	no	—
840	C₂²×C₂₃	—	4	1	no	—
841	C₂²×C₂₃	—	4	1	no	—
842	C₂²×C₂₃	—	4	1	no	—
843	C₂²×C₂₃	—	4	1	no	—
844	C₂²×C₂₃	—	4	1	no	—
845	C₂²×C₂₃	—	4	1	no	—
846	C₂²×C₂₃	—	4	1	no	—
847	C₂²×C₂₃	—	4	1	no	—
848	C₂²×C₂₃	—	4	1	no	—
849	C₂²×C₂₃	—	4	1	no	—
850	C₂²×C₂₃	—	8	4	no	—
851	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
852	C₄×C₂₃	—	2	1	no	—
853	C₄×C₂₃	—	2	1	no	—
854	C₄×C₂₃	—	2	1	no	—
855	C₄×C₂₃	—	2	1	no	—
856	C₄×C₂₃	—	2	1	no	—
857	C₄×C₂₃	—	2	1	no	—
858	C₄×C₂₃	—	2	1	no	—
859	C₄×C₂₃	—	2	1	no	—
860	C₄×C₂₃	—	2	1	no	—
861	C₄×C₂₃	—	2	1	no	—
862	C₄×C₂₃	—	2	1	no	—
863	C₄×C₂₃	—	4	1	no	—
864	C₄×C₂₃	—	4	1	no	—
865	C₄×C₂₃	—	4	1	no	—
866	C₄×C₂₃	—	4	1	no	—
867	C₄×C₂₃	—	4	1	no	—
868	C₄×C₂₃	—	4	1	no	—
869	C₄×C₂₃	—	4	1	no	—
870	C₄×C₂₃	—	4	1	no	—
871	C₄×C₂₃	—	4	1	no	—
872	C₄×C₂₃	—	4	1	no	—
873	C₄×C₂₃	—	4	1	no	—
874	C₄×C₂₃	#585	1	1	yes	characteristic
875	C₄×C₂₃	#585	1	1	yes	characteristic
876	#553	—	2	1	no	—
877	#553	—	2	1	no	—
878	#553	—	2	1	no	—
879	#553	—	2	1	no	—
880	#553	—	2	1	no	—
881	#553	—	2	1	no	—
882	#552	—	2	1	no	—
883	#552	—	2	1	no	—
884	#544	C₂²×C₂₃	1	1	yes	characteristic
885	#542	—	2	1	no	—
886	#542	C₂²×C₂₃	1	1	yes	characteristic
887	#542	C₂²×C₂₃	1	1	yes	characteristic
888	#541	C₂²×C₂₃	1	1	yes	characteristic
889	#541	C₂²×C₂₃	1	1	yes	characteristic, complemented
890	#540	—	2	1	no	—
891	#540	C₂²×C₂₃	1	1	yes	characteristic
892	#540	C₂²×C₂₃	1	1	yes	characteristic
893	#540	C₂²×C₂₃	1	1	yes	characteristic
894	#540	C₂²×C₂₃	1	1	yes	characteristic, complemented
895	#538	—	2	1	no	—
896	#538	—	2	1	no	—
897	#537	C₂²×C₂₃	1	1	yes	characteristic
898	#537	C₂²×C₂₃	1	1	yes	characteristic
899	#537	C₂²×C₂₃	1	1	yes	characteristic
900	#535	C₂²×C₂₃	1	1	yes	characteristic
901	#535	C₂²×C₂₃	1	1	yes	characteristic
902	#532	—	2	1	no	—
903	#532	C₂²×C₂₃	1	1	yes	characteristic
904	#532	C₂²×C₂₃	1	1	yes	characteristic
905	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
906	#529	—	2	1	no	—
907	#529	C₂²×C₂₃	1	1	yes	characteristic
908	#529	C₂²×C₂₃	1	1	yes	characteristic
909	#529	C₂²×C₂₃	1	1	yes	characteristic
910	#529	C₂²×C₂₃	1	1	yes	characteristic
911	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
912	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
913	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
914	#525	—	2	1	no	—
915	#525	—	2	1	no	—
916	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
917	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
918	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
919	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
920	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
921	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
922	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
923	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
924	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
925	#497	C₂²×C₂₃	1	1	yes	characteristic
926	#496	C₂²×C₂₃	1	1	yes	characteristic
927	#493	C₂²×C₂₃	1	1	yes	characteristic
928	#492	C₂²×C₂₃	1	1	yes	characteristic
929	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
930	#490	C₂²×C₂₃	1	1	yes	characteristic
931	#490	C₂²×C₂₃	1	1	yes	characteristic
932	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
933	#488	C₂²×C₂₃	1	1	yes	characteristic
934	#488	C₂²×C₂₃	1	1	yes	characteristic
935	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
936	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
937	#485	C₂²×C₂₃	1	1	yes	characteristic
938	#485	C₂²×C₂₃	1	1	yes	characteristic
939	#484	C₂²×C₂₃	1	1	yes	characteristic
940	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
941	#483	C₂²×C₂₃	1	1	yes	characteristic
942	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
943	#482	C₂²×C₂₃	1	1	yes	characteristic
944	#482	C₂²×C₂₃	1	1	yes	characteristic
945	#481	C₂²×C₂₃	1	1	yes	characteristic
946	#481	C₂²×C₂₃	1	1	yes	characteristic
947	#481	C₂²×C₂₃	1	1	yes	characteristic
948	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
949	#480	C₂²×C₂₃	1	1	yes	characteristic
950	#480	C₂²×C₂₃	1	1	yes	characteristic
951	#480	C₂²×C₂₃	1	1	yes	characteristic
952	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
953	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
954	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
955	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
956	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
957	#478	C₂²×C₂₃	1	1	yes	characteristic
958	#478	C₂²×C₂₃	1	1	yes	characteristic
959	#478	C₂²×C₂₃	1	1	yes	characteristic
960	#478	C₂²×C₂₃	1	1	yes	characteristic
961	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
962	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
963	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
964	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
965	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
966	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
967	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
968	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
969	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
970	#469	C₂²×C₂₃	1	1	yes	characteristic
971	#469	C₂²×C₂₃	1	1	yes	characteristic
972	#469	C₂²×C₂₃	1	1	yes	characteristic, complemented
973	#468	C₂²×C₂₃	1	1	yes	characteristic
974	#468	C₂²×C₂₃	1	1	yes	characteristic
975	#468	C₂²×C₂₃	1	1	yes	characteristic, complemented
976	#468	C₂²×C₂₃	1	1	yes	characteristic, complemented
977	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
978	#466	C₂²×C₂₃	1	1	yes	characteristic
979	#466	C₂²×C₂₃	1	1	yes	characteristic
980	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
981	#465	C₂²×C₂₃	1	1	yes	characteristic
982	#465	C₂²×C₂₃	1	1	yes	characteristic
983	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
984	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
985	#464	C₂²×C₂₃	1	1	yes	characteristic
986	#464	C₂²×C₂₃	1	1	yes	characteristic
987	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
988	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
989	#463	C₂²×C₂₃	1	1	yes	characteristic
990	#463	C₂²×C₂₃	1	1	yes	characteristic
991	#463	C₂²×C₂₃	1	1	yes	characteristic
992	#463	C₂²×C₂₃	1	1	yes	characteristic
993	#463	C₂²×C₂₃	1	1	yes	characteristic
994	#463	C₂²×C₂₃	1	1	yes	characteristic
995	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
996	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
997	#460	C₂²×C₂₃	1	1	yes	characteristic
998	#460	C₂²×C₂₃	1	1	yes	characteristic
999	#459	C₂²×C₂₃	1	1	yes	characteristic
1000	#459	C₂²×C₂₃	1	1	yes	characteristic
1001	#452	C₂²×C₂₃	1	1	yes	characteristic
1002	#452	C₂²×C₂₃	1	1	yes	characteristic
1003	#452	C₂²×C₂₃	1	1	yes	characteristic, complemented
1004	#452	C₂²×C₂₃	1	1	yes	characteristic, complemented
1005	#450	C₂²×C₂₃	1	1	yes	characteristic
1006	#450	C₂²×C₂₃	1	1	yes	characteristic
1007	#449	C₂²×C₂₃	1	1	yes	characteristic
1008	#449	C₂²×C₂₃	1	1	yes	characteristic
1009	#449	C₂²×C₂₃	1	1	yes	characteristic
1010	#449	C₂²×C₂₃	1	1	yes	characteristic
1011	#449	C₂²×C₂₃	1	1	yes	characteristic
1012	#449	C₂²×C₂₃	1	1	yes	characteristic
1013	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
1014	#449	C₂²×C₂₃	1	1	yes	characteristic, complemented
1015	#447	C₂²×C₂₃	1	1	yes	characteristic
1016	#447	C₂²×C₂₃	1	1	yes	characteristic
1017	#442	C₂²×C₂₃	1	1	yes	characteristic
1018	#442	C₂²×C₂₃	1	1	yes	characteristic
1019	#442	C₂²×C₂₃	1	1	yes	characteristic, complemented
1020	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
1021	#440	C₂²×C₂₃	1	1	yes	characteristic
1022	#440	C₂²×C₂₃	1	1	yes	characteristic
1023	#440	C₂²×C₂₃	1	1	yes	characteristic, complemented
1024	#440	C₂²×C₂₃	1	1	yes	characteristic, complemented
1025	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
1026	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
1027	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
1028	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
1029	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
1030	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
1031	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
1032	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
1033	#433	C₂²×C₂₃	1	1	yes	characteristic
1034	#433	C₂²×C₂₃	1	1	yes	characteristic
1035	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
1036	#433	C₂²×C₂₃	1	1	yes	characteristic, complemented
1037	#432	C₂²×C₂₃	1	1	yes	characteristic
1038	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
1039	#431	C₂²×C₂₃	1	1	yes	characteristic
1040	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
1041	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
1042	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
1043	#408	C₂²×C₂₃	1	1	yes	characteristic
1044	#408	C₂²×C₂₃	1	1	yes	characteristic
1045	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
1046	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
1047	C₂×C₂₃	—	4	1	no	—
1048	C₂×C₂₃	—	4	1	no	—
1049	C₂×C₂₃	—	4	1	no	—
1050	C₂×C₂₃	—	8	1	no	—
1051	C₂×C₂₃	—	8	1	no	—
1052	C₂×C₂₃	—	8	1	no	—
1053	C₂×C₂₃	—	8	1	no	—
1054	C₂×C₂₃	—	8	1	no	—
1055	C₂×C₂₃	#3449	1	1	yes	characteristic
1056	C₂×C₂₃	#3584	1	1	yes	characteristic
1057	C₂×C₂₃	#3585	1	1	yes	characteristic
1058	C₂×#41	—	2	1	no	—
1059	C₂×#41	—	2	1	no	—
1060	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1061	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1062	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1063	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1064	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1065	C₂³×C₄	—	2	1	no	—
1066	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
1067	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
1068	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1069	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1070	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1071	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1072	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1073	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1074	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1075	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1076	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1077	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1078	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1079	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1080	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1081	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1082	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
1083	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
1084	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
1085	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
1086	C₄⋊Q₈	—	2	1	no	—
1087	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1088	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1089	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1090	#127	—	2	1	no	—
1091	#127	C₂³×C₂₃	1	1	yes	characteristic
1092	#127	C₂³×C₂₃	1	1	yes	characteristic
1093	#127	C₂³×C₂₃	1	1	yes	characteristic
1094	#126	—	2	1	no	—
1095	#126	—	2	1	no	—
1096	#126	—	2	1	no	—
1097	#126	—	2	1	no	—
1098	#126	—	2	1	no	—
1099	#126	—	2	1	no	—
1100	#126	—	2	1	no	—
1101	#126	—	2	1	no	—
1102	#126	—	2	1	no	—
1103	#126	—	2	1	no	—
1104	#126	—	2	1	no	—
1105	#126	—	2	1	no	—
1106	#125	—	2	1	no	—
1107	#125	—	2	1	no	—
1108	#125	—	2	1	no	—
1109	#125	—	2	1	no	—
1110	#125	—	2	1	no	—
1111	#125	—	2	1	no	—
1112	#125	—	2	1	no	—
1113	#125	C₂³×C₂₃	1	1	yes	characteristic
1114	#125	C₂³×C₂₃	1	1	yes	characteristic
1115	#125	C₂³×C₂₃	1	1	yes	characteristic
1116	#125	C₂³×C₂₃	1	1	yes	characteristic
1117	#125	C₂³×C₂₃	1	1	yes	characteristic
1118	#125	C₂³×C₂₃	1	1	yes	characteristic
1119	#124	—	2	1	no	—
1120	#124	—	2	1	no	—
1121	#124	—	2	1	no	—
1122	#124	—	2	1	no	—
1123	#124	—	2	1	no	—
1124	#124	C₂³×C₂₃	1	1	yes	characteristic
1125	#124	C₂³×C₂₃	1	1	yes	characteristic
1126	#124	C₂³×C₂₃	1	1	yes	characteristic
1127	#124	C₂³×C₂₃	1	1	yes	characteristic
1128	#123	—	2	1	no	—
1129	#123	—	2	1	no	—
1130	#123	—	2	1	no	—
1131	#123	—	2	1	no	—
1132	#123	—	2	1	no	—
1133	#123	—	2	1	no	—
1134	#123	—	2	1	no	—
1135	#123	—	2	1	no	—
1136	#123	—	2	1	no	—
1137	#123	—	2	1	no	—
1138	#123	—	2	1	no	—
1139	#123	—	2	1	no	—
1140	#123	—	2	1	no	—
1141	#123	—	2	1	no	—
1142	#123	—	2	1	no	—
1143	#123	—	2	1	no	—
1144	C₂²⋊Q₈	—	2	1	no	—
1145	C₂²⋊Q₈	—	2	1	no	—
1146	C₂²⋊Q₈	—	2	1	no	—
1147	C₂²⋊Q₈	—	2	1	no	—
1148	C₂²⋊Q₈	—	2	1	no	—
1149	C₂²⋊Q₈	—	2	1	no	—
1150	C₂²⋊Q₈	—	2	1	no	—
1151	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1152	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1153	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1154	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1155	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1156	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	—	2	1	no	—
1160	#121	—	2	1	no	—
1161	#121	—	2	1	no	—
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	—	2	1	no	—
1165	#121	—	2	1	no	—
1166	#121	—	2	1	no	—
1167	#121	—	2	1	no	—
1168	#121	—	2	1	no	—
1169	#121	—	2	1	no	—
1170	#121	—	2	1	no	—
1171	#121	—	2	1	no	—
1172	#121	—	2	1	no	—
1173	#121	—	2	1	no	—
1174	#121	—	2	1	no	—
1175	#121	—	2	1	no	—
1176	#121	—	2	1	no	—
1177	#121	—	2	1	no	—
1178	#121	—	2	1	no	—
1179	#121	—	2	1	no	—
1180	#121	C₂³×C₂₃	1	1	yes	characteristic
1181	#121	C₂³×C₂₃	1	1	yes	characteristic
1182	#121	C₂³×C₂₃	1	1	yes	characteristic
1183	#121	C₂³×C₂₃	1	1	yes	characteristic
1184	#121	C₂³×C₂₃	1	1	yes	characteristic
1185	#121	C₂³×C₂₃	1	1	yes	characteristic
1186	#121	C₂³×C₂₃	1	1	yes	characteristic
1187	#121	C₂³×C₂₃	1	1	yes	characteristic
1188	#121	C₂³×C₂₃	1	1	yes	characteristic
1189	#121	C₂³×C₂₃	1	1	yes	characteristic
1190	#120	—	2	1	no	—
1191	#120	—	2	1	no	—
1192	#120	—	2	1	no	—
1193	#120	—	2	1	no	—
1194	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
1195	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
1196	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1197	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1198	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1199	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1200	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1201	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1202	C₄×D₄	—	2	1	no	—
1203	C₄×D₄	—	2	1	no	—
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	—	2	1	no	—
1208	C₄×D₄	—	2	1	no	—
1209	C₄×D₄	—	2	1	no	—
1210	C₄×D₄	—	2	1	no	—
1211	C₄×D₄	—	2	1	no	—
1212	C₄×D₄	—	2	1	no	—
1213	C₄×D₄	—	2	1	no	—
1214	C₄×D₄	—	2	1	no	—
1215	C₄×D₄	—	2	1	no	—
1216	C₄×D₄	—	2	1	no	—
1217	C₄×D₄	—	2	1	no	—
1218	C₄×D₄	—	2	1	no	—
1219	C₄×D₄	—	2	1	no	—
1220	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1221	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1222	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1223	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1224	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1225	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
1226	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1227	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1228	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1229	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1230	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1231	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1232	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1233	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1234	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1235	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1236	#117	—	2	1	no	—
1237	#117	—	2	1	no	—
1238	#117	—	2	1	no	—
1239	#117	—	2	1	no	—
1240	#117	—	2	1	no	—
1241	#117	—	2	1	no	—
1242	#117	—	2	1	no	—
1243	#117	—	2	1	no	—
1244	#117	—	2	1	no	—
1245	#117	C₂³×C₂₃	1	1	yes	characteristic
1246	#117	C₂³×C₂₃	1	1	yes	characteristic
1247	#117	C₂³×C₂₃	1	1	yes	characteristic
1248	#117	C₂³×C₂₃	1	1	yes	characteristic
1249	C₂×C₄⋊C₄	—	2	1	no	—
1250	C₂×C₄⋊C₄	—	2	1	no	—
1251	C₂×C₄⋊C₄	—	2	1	no	—
1252	C₂×C₄⋊C₄	—	2	1	no	—
1253	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1254	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1255	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1256	C₂×C₂²⋊C₄	—	2	1	no	—
1257	C₂×C₄²	—	2	1	no	—
1258	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1259	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1260	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1261	#107	C₂³×C₂₃	1	1	yes	characteristic
1262	#107	C₂³×C₂₃	1	1	yes	characteristic
1263	#107	C₂³×C₂₃	1	1	yes	characteristic
1264	#107	C₂³×C₂₃	1	1	yes	characteristic
1265	#107	C₂³×C₂₃	1	1	yes	characteristic
1266	#107	C₂³×C₂₃	1	1	yes	characteristic
1267	#107	C₂³×C₂₃	1	1	yes	characteristic
1268	#107	C₂³×C₂₃	1	1	yes	characteristic
1269	#106	C₂³×C₂₃	1	1	yes	characteristic
1270	#106	C₂³×C₂₃	1	1	yes	characteristic
1271	#106	C₂³×C₂₃	1	1	yes	characteristic
1272	#106	C₂³×C₂₃	1	1	yes	characteristic
1273	#106	C₂³×C₂₃	1	1	yes	characteristic
1274	#106	C₂³×C₂₃	1	1	yes	characteristic
1275	#106	C₂³×C₂₃	1	1	yes	characteristic
1276	#106	C₂³×C₂₃	1	1	yes	characteristic
1277	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1278	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1279	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1280	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1281	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1282	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1283	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1284	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1285	#103	C₂³×C₂₃	1	1	yes	characteristic
1286	#103	C₂³×C₂₃	1	1	yes	characteristic
1287	#103	C₂³×C₂₃	1	1	yes	characteristic
1288	#103	C₂³×C₂₃	1	1	yes	characteristic
1289	#103	C₂³×C₂₃	1	1	yes	characteristic
1290	#103	C₂³×C₂₃	1	1	yes	characteristic
1291	#103	C₂³×C₂₃	1	1	yes	characteristic
1292	#103	C₂³×C₂₃	1	1	yes	characteristic
1293	#103	C₂³×C₂₃	1	1	yes	characteristic
1294	#103	C₂³×C₂₃	1	1	yes	characteristic
1295	#103	C₂³×C₂₃	1	1	yes	characteristic
1296	#103	C₂³×C₂₃	1	1	yes	characteristic
1297	#102	C₂³×C₂₃	1	1	yes	characteristic
1298	#102	C₂³×C₂₃	1	1	yes	characteristic
1299	#102	C₂³×C₂₃	1	1	yes	characteristic
1300	#102	C₂³×C₂₃	1	1	yes	characteristic
1301	#102	C₂³×C₂₃	1	1	yes	characteristic
1302	#102	C₂³×C₂₃	1	1	yes	characteristic
1303	#102	C₂³×C₂₃	1	1	yes	characteristic
1304	#102	C₂³×C₂₃	1	1	yes	characteristic
1305	#102	C₂³×C₂₃	1	1	yes	characteristic
1306	#102	C₂³×C₂₃	1	1	yes	characteristic
1307	#102	C₂³×C₂₃	1	1	yes	characteristic
1308	#102	C₂³×C₂₃	1	1	yes	characteristic
1309	#102	C₂³×C₂₃	1	1	yes	characteristic
1310	#102	C₂³×C₂₃	1	1	yes	characteristic
1311	#102	C₂³×C₂₃	1	1	yes	characteristic
1312	#102	C₂³×C₂₃	1	1	yes	characteristic
1313	#102	C₂³×C₂₃	1	1	yes	characteristic
1314	#102	C₂³×C₂₃	1	1	yes	characteristic
1315	#102	C₂³×C₂₃	1	1	yes	characteristic
1316	#102	C₂³×C₂₃	1	1	yes	characteristic
1317	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1318	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1319	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1320	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1321	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1322	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1323	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1324	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1325	#97	C₂³×C₂₃	1	1	yes	characteristic
1326	#97	C₂³×C₂₃	1	1	yes	characteristic
1327	#97	C₂³×C₂₃	1	1	yes	characteristic
1328	#97	C₂³×C₂₃	1	1	yes	characteristic
1329	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1330	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1331	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1332	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1333	C₂₃	#60997	1	1	yes	characteristic, direct product factor, Sylow
1334	C₂⁴	—	2	1	no	—
1335	#41	—	4	1	no	—
1336	#41	—	4	1	no	—
1337	#41	—	4	1	no	—
1338	#41	—	4	1	no	—
1339	#41	—	4	1	no	—
1340	#41	—	4	1	no	—
1341	#41	—	4	1	no	—
1342	#41	—	4	1	no	—
1343	#41	—	8	2	no	—
1344	#41	—	8	2	no	—
1345	C₂×Q₈	—	2	1	no	—
1346	C₂×Q₈	—	2	1	no	—
1347	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1348	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1349	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1350	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1351	C₂×D₄	—	2	1	no	—
1352	C₂×D₄	—	2	1	no	—
1353	C₂×D₄	—	2	1	no	—
1354	C₂×D₄	—	2	1	no	—
1355	C₂×D₄	—	2	1	no	—
1356	C₂×D₄	—	2	1	no	—
1357	C₂×D₄	—	2	1	no	—
1358	C₂×D₄	—	2	1	no	—
1359	C₂×D₄	—	2	1	no	—
1360	C₂×D₄	—	2	1	no	—
1361	C₂×D₄	—	2	1	no	—
1362	C₂×D₄	—	2	1	no	—
1363	C₂×D₄	—	2	1	no	—
1364	C₂×D₄	—	2	1	no	—
1365	C₂×D₄	—	2	1	no	—
1366	C₂×D₄	—	2	1	no	—
1367	C₂×D₄	—	2	1	no	—
1368	C₂×D₄	—	2	1	no	—
1369	C₂×D₄	—	2	1	no	—
1370	C₂×D₄	—	2	1	no	—
1371	C₂×D₄	—	4	1	no	—
1372	C₂×D₄	—	4	1	no	—
1373	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1374	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1375	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1376	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1377	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1378	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1379	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1380	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1381	C₂²×C₄	—	2	1	no	—
1382	C₂²×C₄	—	2	1	no	—
1383	C₂²×C₄	—	2	1	no	—
1384	C₂²×C₄	—	2	1	no	—
1385	C₂²×C₄	—	2	1	no	—
1386	C₂²×C₄	—	2	1	no	—
1387	C₂²×C₄	—	2	1	no	—
1388	C₂²×C₄	—	2	1	no	—
1389	C₂²×C₄	—	2	1	no	—
1390	C₂²×C₄	—	2	1	no	—
1391	C₂²×C₄	—	2	1	no	—
1392	C₂²×C₄	—	2	1	no	—
1393	C₂²×C₄	—	2	1	no	—
1394	C₂²×C₄	—	2	1	no	—
1395	C₂²×C₄	—	2	1	no	—
1396	C₂²×C₄	—	2	1	no	—
1397	C₂²×C₄	—	8	2	no	—
1398	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1399	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1400	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1401	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1402	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1403	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1404	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1405	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1406	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1407	Q₁₆	—	4	1	no	—
1408	Q₁₆	—	4	1	no	—
1409	SD₁₆	—	4	1	no	—
1410	SD₁₆	—	4	1	no	—
1411	SD₁₆	—	4	1	no	—
1412	SD₁₆	—	4	1	no	—
1413	SD₁₆	—	4	1	no	—
1414	SD₁₆	—	4	1	no	—
1415	SD₁₆	—	4	1	no	—
1416	SD₁₆	—	4	1	no	—
1417	D₈	—	4	1	no	—
1418	D₈	—	4	1	no	—
1419	D₈	—	4	1	no	—
1420	D₈	—	4	1	no	—
1421	D₈	—	4	1	no	—
1422	D₈	—	4	1	no	—
1423	M₁₆	—	4	1	no	—
1424	M₁₆	—	4	1	no	—
1425	C₂×C₈	—	4	1	no	—
1426	C₂×C₈	—	4	1	no	—
1427	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1428	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1429	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1430	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1431	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1432	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1433	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1434	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	—	2	1	no	—
1450	C₄⋊C₄	—	2	1	no	—
1451	C₄⋊C₄	—	2	1	no	—
1452	C₄⋊C₄	—	2	1	no	—
1453	C₄⋊C₄	—	2	1	no	—
1454	C₄⋊C₄	—	2	1	no	—
1455	C₄⋊C₄	—	2	1	no	—
1456	C₄⋊C₄	—	2	1	no	—
1457	C₄⋊C₄	—	2	1	no	—
1458	C₄⋊C₄	—	2	1	no	—
1459	C₄⋊C₄	—	2	1	no	—
1460	C₄⋊C₄	—	2	1	no	—
1461	C₄⋊C₄	—	2	1	no	—
1462	C₄⋊C₄	—	2	1	no	—
1463	C₄⋊C₄	—	2	1	no	—
1464	C₄⋊C₄	—	2	1	no	—
1465	C₄⋊C₄	—	2	1	no	—
1466	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1467	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1468	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1469	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1470	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1471	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1472	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1473	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1474	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1475	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1476	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1477	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1478	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1479	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	—	2	1	no	—
1496	C₂²⋊C₄	—	2	1	no	—
1497	C₂²⋊C₄	—	2	1	no	—
1498	C₂²⋊C₄	—	2	1	no	—
1499	C₂²⋊C₄	—	2	1	no	—
1500	C₂²⋊C₄	—	2	1	no	—
1501	C₂²⋊C₄	—	2	1	no	—
1502	C₂²⋊C₄	—	2	1	no	—
1503	C₂²⋊C₄	—	2	1	no	—
1504	C₂²⋊C₄	—	2	1	no	—
1505	C₂²⋊C₄	—	2	1	no	—
1506	C₂²⋊C₄	—	2	1	no	—
1507	C₂²⋊C₄	—	2	1	no	—
1508	C₂²⋊C₄	—	2	1	no	—
1509	C₂²⋊C₄	—	2	1	no	—
1510	C₂²⋊C₄	—	2	1	no	—
1511	C₂²⋊C₄	—	2	1	no	—
1512	C₂²⋊C₄	—	2	1	no	—
1513	C₂²⋊C₄	—	2	1	no	—
1514	C₂²⋊C₄	—	2	1	no	—
1515	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1516	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1517	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1518	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1519	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1520	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1521	C₄²	—	2	1	no	—
1522	C₄²	—	2	1	no	—
1523	C₄²	—	2	1	no	—
1524	C₄²	—	2	1	no	—
1525	C₄²	—	2	1	no	—
1526	C₄²	—	2	1	no	—
1527	C₄²	—	2	1	no	—
1528	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1529	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1530	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1531	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1532	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1533	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1534	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1535	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1536	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1537	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1538	C₂³	—	2	1	no	—
1539	C₂³	—	2	1	no	—
1540	C₂³	—	2	1	no	—
1541	C₂³	—	2	1	no	—
1542	C₂³	—	2	1	no	—
1543	C₂³	—	4	2	no	—
1544	C₂³	—	8	1	no	—
1545	C₂³	—	8	1	no	—
1546	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1547	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1548	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1549	Q₈	—	2	1	no	—
1550	Q₈	—	2	1	no	—
1551	Q₈	—	2	1	no	—
1552	Q₈	—	2	1	no	—
1553	Q₈	—	2	1	no	—
1554	Q₈	—	2	1	no	—
1555	Q₈	—	4	1	no	—
1556	Q₈	—	8	1	no	—
1557	Q₈	—	8	1	no	—
1558	D₄	—	2	1	no	—
1559	D₄	—	2	1	no	—
1560	D₄	—	2	1	no	—
1561	D₄	—	2	1	no	—
1562	D₄	—	2	1	no	—
1563	D₄	—	2	1	no	—
1564	D₄	—	2	1	no	—
1565	D₄	—	2	1	no	—
1566	D₄	—	2	1	no	—
1567	D₄	—	2	1	no	—
1568	D₄	—	4	1	no	—
1569	D₄	—	4	1	no	—
1570	D₄	—	4	1	no	—
1571	D₄	—	4	2	no	—
1572	D₄	—	4	2	no	—
1573	D₄	—	4	2	no	—
1574	D₄	—	4	2	no	—
1575	D₄	—	8	1	no	—
1576	D₄	—	8	1	no	—
1577	D₄	—	8	1	no	—
1578	D₄	—	8	1	no	—
1579	D₄	—	8	1	no	—
1580	D₄	—	8	1	no	—
1581	D₄	—	8	1	no	—
1582	D₄	—	8	1	no	—
1583	D₄	—	8	1	no	—
1584	D₄	—	8	1	no	—
1585	D₄	—	8	1	no	—
1586	D₄	—	8	1	no	—
1587	D₄	—	8	1	no	—
1588	D₄	—	8	1	no	—
1589	D₄	—	8	1	no	—
1590	D₄	—	8	1	no	—
1591	C₂×C₄	—	2	1	no	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	2	1	no	—
1599	C₂×C₄	—	2	1	no	—
1600	C₂×C₄	—	2	1	no	—
1601	C₂×C₄	—	2	1	no	—
1602	C₂×C₄	—	2	1	no	—
1603	C₂×C₄	—	2	1	no	—
1604	C₂×C₄	—	2	1	no	—
1605	C₂×C₄	—	2	1	no	—
1606	C₂×C₄	—	2	1	no	—
1607	C₂×C₄	—	2	1	no	—
1608	C₂×C₄	—	4	1	no	—
1609	C₂×C₄	—	4	1	no	—
1610	C₂×C₄	—	4	1	no	—
1611	C₂×C₄	—	4	1	no	—
1612	C₂×C₄	—	4	1	no	—
1613	C₂×C₄	—	4	1	no	—
1614	C₂×C₄	—	4	2	no	—
1615	C₂×C₄	—	4	2	no	—
1616	C₂×C₄	—	4	2	no	—
1617	C₂×C₄	—	4	2	no	—
1618	C₂×C₄	—	4	2	no	—
1619	C₂×C₄	—	4	2	no	—
1620	C₂×C₄	—	8	1	no	—
1621	C₂×C₄	—	8	1	no	—
1622	C₂×C₄	—	8	1	no	—
1623	C₂×C₄	—	8	1	no	—
1624	C₂×C₄	—	8	1	no	—
1625	C₂×C₄	—	8	1	no	—
1626	C₂×C₄	—	8	1	no	—
1627	C₂×C₄	—	8	1	no	—
1628	C₂×C₄	—	8	1	no	—
1629	C₂×C₄	—	8	1	no	—
1630	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1631	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1632	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1633	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1634	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1635	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1636	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1637	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1638	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1639	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1640	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1641	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1642	C₈	—	2	1	no	—
1643	C₈	—	2	1	no	—
1644	C₈	—	2	1	no	—
1645	C₈	—	2	1	no	—
1646	C₈	—	2	1	no	—
1647	C₈	—	2	1	no	—
1648	C₈	—	2	1	no	—
1649	C₈	—	2	1	no	—
1650	C₂²	—	2	1	no	—
1651	C₂²	—	2	1	no	—
1652	C₂²	—	2	1	no	—
1653	C₂²	—	2	1	no	—
1654	C₂²	—	2	1	no	—
1655	C₂²	—	2	1	no	—
1656	C₂²	—	2	1	no	—
1657	C₂²	—	2	1	no	—
1658	C₂²	—	2	1	no	—
1659	C₂²	—	4	1	no	—
1660	C₂²	—	4	1	no	—
1661	C₂²	—	4	1	no	—
1662	C₂²	—	4	1	no	—
1663	C₂²	—	4	1	no	—
1664	C₂²	—	4	1	no	—
1665	C₂²	—	4	1	no	—
1666	C₂²	—	4	1	no	—
1667	C₂²	—	4	1	no	—
1668	C₂²	—	4	1	no	—
1669	C₂²	—	4	1	no	—
1670	C₂²	—	4	1	no	—
1671	C₂²	—	4	1	no	—
1672	C₂²	—	4	1	no	—
1673	C₂²	—	4	1	no	—
1674	C₂²	—	8	4	no	—
1675	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1676	C₄	—	2	1	no	—
1677	C₄	—	2	1	no	—
1678	C₄	—	2	1	no	—
1679	C₄	—	2	1	no	—
1680	C₄	—	2	1	no	—
1681	C₄	—	2	1	no	—
1682	C₄	—	2	1	no	—
1683	C₄	—	2	1	no	—
1684	C₄	—	2	1	no	—
1685	C₄	—	2	1	no	—
1686	C₄	—	2	1	no	—
1687	C₄	—	4	1	no	—
1688	C₄	—	4	1	no	—
1689	C₄	—	4	1	no	—
1690	C₄	—	4	1	no	—
1691	C₄	—	4	1	no	—
1692	C₄	—	4	1	no	—
1693	C₄	—	4	1	no	—
1694	C₄	—	4	1	no	—
1695	C₄	—	4	1	no	—
1696	C₄	—	4	1	no	—
1697	C₄	—	4	1	no	—
1698	C₄	C₂₃×#585	1	1	yes	characteristic
1699	C₄	C₂₃×#585	1	1	yes	characteristic
1700	C₂	—	4	1	no	—
1701	C₂	—	4	1	no	—
1702	C₂	—	4	1	no	—
1703	C₂	—	8	1	no	—
1704	C₂	—	8	1	no	—
1705	C₂	—	8	1	no	—
1706	C₂	—	8	1	no	—
1707	C₂	—	8	1	no	—
1708	C₂	C₂₃×#3449	1	1	yes	characteristic
1709	C₂	C₂₃×#3584	1	1	yes	characteristic
1710	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3512	C₂	semidirect
2. C₂₃×#3460	C₂	semidirect
3. C₂₃×#3256	C₂	semidirect
4. C₂₃×#3251	C₂	semidirect
5. C₂₃×#3250	C₂	semidirect
6. C₂₃×#3247	C₂	semidirect
7. C₂₃×#3242	C₂	semidirect
8. C₂₃×#3241	C₂	semidirect
9. C₂₃×#3234	C₂	semidirect
10. C₂₃×#3232	C₂	semidirect
11. C₂₃×#3222	C₂	semidirect
12. C₂₃×#3220	C₂	semidirect
13. C₂₃×#3219	C₂	semidirect
14. C₂₃×#3207	C₂	semidirect
15. C₂₃×#3204	C₂	semidirect
16. C₂₃×#3203	C₂	semidirect
17. C₂₃×#3198	C₂	semidirect
18. C₂₃×#3198	C₂	semidirect
19. C₂₃×#3179	C₂	semidirect
20. C₂₃×#3178	C₂	semidirect
21. C₂₃×#3176	C₂	semidirect
22. C₂₃×#3174	C₂	semidirect
23. C₂₃×#3125	C₂	semidirect
24. C₂₃×#3124	C₂	semidirect
25. C₂₃×#3119	C₂	semidirect
26. C₂₃×#3119	C₂	semidirect
27. C₂₃×#3114	C₂	semidirect
28. C₂₃×#3111	C₂	semidirect
29. C₂₃×#3105	C₂	semidirect
30. C₂₃×#3102	C₂	semidirect
31. C₂₃×#2925	C₂	semidirect
45. C₂₃×#541	C₂²	semidirect
50. C₂₃×#540	C₂²	semidirect
61. C₂₃×#532	C₂²	semidirect
67. C₂₃×#529	C₂²	semidirect
68. C₂₃×#529	C₂²	semidirect
69. C₂×C₂₃×#125	C₂²	semidirect
72. C₂₃×#520	C₂²	semidirect
73. C₂₃×#520	C₂²	semidirect
77. C₂₃×#501	C₂²	semidirect
78. C₂₃×#501	C₂²	semidirect
79. C₂₃×#499	C₂²	semidirect
80. C₂₃×#499	C₂²	semidirect
85. C₂₃×#491	C₂²	semidirect
88. C₂₃×#490	C₂²	semidirect
91. C₂₃×#487	C₂²	semidirect
92. C₂₃×#486	C₂²	semidirect
96. C₂₃×#484	C₂²	semidirect
98. C₂₃×#483	C₂²	semidirect
104. C₂₃×#481	C₂²	semidirect
108. C₂₃×#480	C₂²	semidirect
109. C₂₃×#479	C₂²	semidirect
110. C₂₃×#479	C₂²	semidirect
111. C₂₃×#479	C₂²	semidirect
112. C₂₃×#479	C₂²	semidirect
117. C₂₃×#478	C₂²	semidirect
118. C₂₃×#478	C₂²	semidirect
119. C₂₃×#478	C₂²	semidirect
120. C₂₃×#478	C₂²	semidirect
121. C₂₃×#477	C₂²	semidirect
122. C₂₃×#476	C₂²	semidirect
123. C₂₃×#475	C₂²	semidirect
124. C₂₃×#474	C₂²	semidirect
125. C₂₃×#470	C₂²	semidirect
128. C₂₃×#469	C₂²	semidirect
131. C₂₃×#468	C₂²	semidirect
132. C₂₃×#468	C₂²	semidirect
133. C₂₃×#467	C₂²	semidirect
136. C₂₃×#466	C₂²	semidirect
139. C₂₃×#465	C₂²	semidirect
140. C₂₃×#465	C₂²	semidirect
143. C₂₃×#464	C₂²	semidirect
144. C₂₃×#464	C₂²	semidirect
151. C₂₃×#463	C₂²	semidirect
152. C₂₃×#463	C₂²	semidirect
159. C₂₃×#452	C₂²	semidirect
160. C₂₃×#452	C₂²	semidirect
169. C₂₃×#449	C₂²	semidirect
170. C₂₃×#449	C₂²	semidirect
175. C₂₃×#442	C₂²	semidirect
176. C₂₃×#441	C₂²	semidirect
179. C₂₃×#440	C₂²	semidirect
180. C₂₃×#440	C₂²	semidirect
181. C₄×Q₁₆×C₂₃	C₂²	semidirect
184. C₄×SD₁₆×C₂₃	C₂²	semidirect
185. C₄×SD₁₆×C₂₃	C₂²	semidirect
188. C₄×D₈×C₂₃	C₂²	semidirect
191. C₂₃×#433	C₂²	semidirect
192. C₂₃×#433	C₂²	semidirect
194. C₂₃×#432	C₂²	semidirect
196. C₂₃×#431	C₂²	semidirect
197. C₂₃×#423	C₂²	semidirect
198. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
201. C₂₃×#405	C₂²	semidirect
202. C₂₃×#405	C₂²	semidirect
682. #60997	C₂₃	direct (N × H)
795. #3512	C₂×C₂₃	semidirect
796. #3460	C₂×C₂₃	semidirect
797. #3256	C₂×C₂₃	semidirect
798. #3251	C₂×C₂₃	semidirect
799. #3250	C₂×C₂₃	semidirect
800. #3247	C₂×C₂₃	semidirect
801. #3242	C₂×C₂₃	semidirect
802. #3241	C₂×C₂₃	semidirect
803. #3234	C₂×C₂₃	semidirect
804. #3232	C₂×C₂₃	semidirect
805. #3222	C₂×C₂₃	semidirect
806. #3220	C₂×C₂₃	semidirect
807. #3219	C₂×C₂₃	semidirect
808. #3207	C₂×C₂₃	semidirect
809. #3204	C₂×C₂₃	semidirect
810. #3203	C₂×C₂₃	semidirect
811. #3198	C₂×C₂₃	semidirect
812. #3198	C₂×C₂₃	semidirect
813. #3179	C₂×C₂₃	semidirect
814. #3178	C₂×C₂₃	semidirect
815. #3176	C₂×C₂₃	semidirect
816. #3174	C₂×C₂₃	semidirect
817. #3125	C₂×C₂₃	semidirect
818. #3124	C₂×C₂₃	semidirect
819. #3119	C₂×C₂₃	semidirect
820. #3119	C₂×C₂₃	semidirect
821. #3114	C₂×C₂₃	semidirect
822. #3111	C₂×C₂₃	semidirect
823. #3105	C₂×C₂₃	semidirect
824. #3102	C₂×C₂₃	semidirect
825. #2925	C₂×C₂₃	semidirect
889. #541	C₂²×C₂₃	semidirect
894. #540	C₂²×C₂₃	semidirect
905. #532	C₂²×C₂₃	semidirect
911. #529	C₂²×C₂₃	semidirect
912. #529	C₂²×C₂₃	semidirect
913. C₂×#125	C₂²×C₂₃	semidirect
916. #520	C₂²×C₂₃	semidirect
917. #520	C₂²×C₂₃	semidirect
921. #501	C₂²×C₂₃	semidirect
922. #501	C₂²×C₂₃	semidirect
923. #499	C₂²×C₂₃	semidirect
924. #499	C₂²×C₂₃	semidirect
929. #491	C₂²×C₂₃	semidirect
932. #490	C₂²×C₂₃	semidirect
935. #487	C₂²×C₂₃	semidirect
936. #486	C₂²×C₂₃	semidirect
940. #484	C₂²×C₂₃	semidirect
942. #483	C₂²×C₂₃	semidirect
948. #481	C₂²×C₂₃	semidirect
952. #480	C₂²×C₂₃	semidirect
953. #479	C₂²×C₂₃	semidirect
954. #479	C₂²×C₂₃	semidirect
955. #479	C₂²×C₂₃	semidirect
956. #479	C₂²×C₂₃	semidirect
961. #478	C₂²×C₂₃	semidirect
962. #478	C₂²×C₂₃	semidirect
963. #478	C₂²×C₂₃	semidirect
964. #478	C₂²×C₂₃	semidirect
965. #477	C₂²×C₂₃	semidirect
966. #476	C₂²×C₂₃	semidirect
967. #475	C₂²×C₂₃	semidirect
968. #474	C₂²×C₂₃	semidirect
969. #470	C₂²×C₂₃	semidirect
972. #469	C₂²×C₂₃	semidirect
975. #468	C₂²×C₂₃	semidirect
976. #468	C₂²×C₂₃	semidirect
977. #467	C₂²×C₂₃	semidirect
980. #466	C₂²×C₂₃	semidirect
983. #465	C₂²×C₂₃	semidirect
984. #465	C₂²×C₂₃	semidirect
987. #464	C₂²×C₂₃	semidirect
988. #464	C₂²×C₂₃	semidirect
995. #463	C₂²×C₂₃	semidirect
996. #463	C₂²×C₂₃	semidirect
1003. #452	C₂²×C₂₃	semidirect
1004. #452	C₂²×C₂₃	semidirect
1013. #449	C₂²×C₂₃	semidirect
1014. #449	C₂²×C₂₃	semidirect
1019. #442	C₂²×C₂₃	semidirect
1020. #441	C₂²×C₂₃	semidirect
1023. #440	C₂²×C₂₃	semidirect
1024. #440	C₂²×C₂₃	semidirect
1025. C₄×Q₁₆	C₂²×C₂₃	semidirect
1028. C₄×SD₁₆	C₂²×C₂₃	semidirect
1029. C₄×SD₁₆	C₂²×C₂₃	semidirect
1032. C₄×D₈	C₂²×C₂₃	semidirect
1035. #433	C₂²×C₂₃	semidirect
1036. #433	C₂²×C₂₃	semidirect
1038. #432	C₂²×C₂₃	semidirect
1040. #431	C₂²×C₂₃	semidirect
1041. #423	C₂²×C₂₃	semidirect
1042. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
1045. #405	C₂²×C₂₃	semidirect
1046. #405	C₂²×C₂₃	semidirect
1333. C₂₃	#60997	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3512	2
C₂₃×#3460	2
C₂₃×#3256	2
C₂₃×#3251	2
C₂₃×#3250	2
C₂₃×#3247	2
C₂₃×#3242	2
C₂₃×#3241	2
C₂₃×#3234	2
C₂₃×#3232	2
C₂₃×#3222	2
C₂₃×#3220	2
C₂₃×#3219	2
C₂₃×#3207	2
C₂₃×#3204	2
C₂₃×#3203	2
C₂₃×#3198	2
C₂₃×#3179	2
C₂₃×#3178	2
C₂₃×#3176	2
C₂₃×#3174	2
C₂₃×#3125	2
C₂₃×#3124	2
C₂₃×#3119	2
C₂₃×#3114	2
C₂₃×#3111	2
C₂₃×#3105	2
C₂₃×#3102	2
C₂₃×#2925	2
#60997	23

Subgroups — C23×#60997 #19208623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60997 #19208623